Appendix II. 857 And, slope ordinate = (stress sum-curve ordinate) — Ey Thus the slope curve s may be drawn by summating the stress curve, and then dividing by Ey. Again, if A B be made very small, the angle a = VA B, and tan a = average slope between A B. Then, Deflection at B = D tana = D (average slope A to B). Similarly the angle (a + /3) = inclination of B c to A v, and tan (a + /3) = average slope between B c. Then, Total deflection at c = D tan a -I- F tan (a -h/3) = D (slope A B) -f F (slope B c) = ef+gh And, sum of slope curve 1 __ f Total deflection to any point J """ \ at that point. The problem is therefore completed by drawing the deflection curve A as the summation of slope curve area, and the general formula is deduced for a beam of uniform section : Deflection - *<«=) _ S(SBJ ZEy El To prove that the maximum deflection of a cantilever with concentrated load = W/3/3El (p.451): the Bm curve is triangular, whose sum = W/2/2, and this is the maximum slope. But the slope curve is a parabola, whose area is therefore |- W/2/2x/ viz., W /3/3, which is the second summation of the Bm; and by above general formula, deflection = W /3/3 E I. Some care is required in fixing scales, but previous explana- tions may be consulted. When beam section varies, Z will alter also, and the stress curve must be found : then continue as before. Note that load^ shear, Bm , slope^ and deflection curves are a con- tinuous series, where each is the sum or integral of the preceding one. P. 458. Pillars and Struts.—In the paper cited on p. 458, Prof. Fidler assigns various reasons why pillar strength cannot be shewn practically by Euler's formula, such as an in- constant E, even in the same strut, and initial curvature in line of thrust, the latter altering W considerably. In Fig. 820 the crosses shew Christie's experiments on T bars, and the small circles